Blender 2.8 I want to select the vertices, edges and faces that are on the front ONLY
There are several approaches you could take.
Note: So far as I can find, the backface culling options don't seem to do the trick. The one in the Materials tab, under the Settings section, would seem to only affect the appearance of backfaces during rendering. But there is another Backface Culling option located under the Viewport Shading menu at the top right of the 3D View, and it is only accessible if you happen to be in Solid shading mode at the moment. Clicking the Backface Culling checkbox here makes the backfaces change to translucent, but doesn't prevent their selection. One could be forgiven for expecting either of these options to prevent selection of backfaces, but neither do. The latter doesn't seem to do anything.
Thankfully, there are other approaches.

By default, your objects in a new scene are in solid shade mode. When
you go into Edit Mode for any object, it is likewise solid shaded by
default. If you go into Wireframe shading mode for the object while
it is in Edit Mode, you will see through the object, and be able to
select vertices on both sides. But if you press Alt +
z, you will toggle the X-ray feature for the mesh. This
feature works in both Object Mode and Edit Mode. In Edit Mode, it
forces an opaque view of the mesh in wireframe shading mode, where
normally, it would be transparent when the wireframe shows. This can
help prevent vertex selections to the rear of the mesh.
Alternatively, you can press Alt + b at any
time and then drag a box to create a View Clipping boundary, which
can be used to coral any parts that you want exclusively visible, meaning it instantly hides everything outside the boundary from
view. Pressing Alt + b again gets rid of the boundary.
Another interesting thing to note: For addressing this kind of issue specifically
during dyntopo, there is a common workflow in Blender where one
temporarily adds a Solidify modifier to the main mesh. The reason
for this is that the Solidify modifier simulates the existence of
both an outer shell facing and an inner shell facing, which includes
the simulated behavior of face normals. By having a Solidify modifier
in place, then when going into Edit Mode, the inner shell on the opposite side of the object
behaves as if it were an outer shell instead. This tricks
Blender into ignoring those faces during selection, effectively
giving you backface culling in Edit Mode even if you can't get it any
other way.